Properties of Exponents
Simplify the Expression. Use only positive exponents. (y3)(y-5)
1/(y2)
A cat population of 200 is increasing at a rate of 20% per month. What equation would represent the cat's population, y, after x amount of months?
y= 200(1.2)x
y = 200(1+0.20)x
Determine whether the table represents growth or decay.
| x | 0 | 1 | 2 | 3 |
| y | 3 | 6 | 12 | 24 |
exponential growth
What is the common ratio for the sequence 81, 27, 9...
r=1/3
Is f(x)=3(4)x growth or decay?
Growth
Simplify the Expression. Use only positive exponents. (x4)/(x7)
1/(x3)
The equation y =3000(1.3)x represent the population of some ducks after x years. Identify the initial population of ducks, and the growth rate
Initial population is 3,000.
The growth rate is 30% per year.
A new car cost $25,000 and depreciates at a rate of 20% per year. What function could model the value of the car after x years?
y=25,000(0.80)x
What is the explicit formula for the sequence 10, 7, 4...?
an=-3n+13
an = 10 -3(n-1)
Titanium-51 decays with a half life of 6 minutes. If you started with 1024 grams of titanium-51, how much would remain after one hour?
1 gram
Simplify the Expression. Use only positive exponents. (x0y2)3
y6
The initial population of a bacteria is 3,000. It is growing at a rate of 32% per hour. How much bacteria are there after 1 day?
2,349,068 bacteria.
The function y=13,000(0.75)x represents the value of a used car after x years. Identify the initial value of the car and the rate of decay
13,000 is initial value of the car and 25% per year is the decay rate.
An auditorium had 30 chairs in the first row, 35 in the second row, 40 in the 3rd row,.... all the way up to the 30th row. How many chairs are in the 25th row?
150 chairs
Find the average rate of change from x=5 to x=7 for the function f(x)=0.10(2)x.
4.8
Simplify the expression...
4a2b5c / 2a4b2c
2b3 / a2
If the function f(x)=8(3)x is changed to f(x)=8(3)x+7, how will the graph change?
The graph will shift 7 units up.
From an equation, how can you tell if an exponential function is decaying ?
The common multiplier/ratio is a number between 0 and 1.
Write an explicit equation for the nth term. 1,4,16,64,...
an=4n-1 or an= (1/4) 4n
You invested $52,400 at 6% compounded annually for 5 years. What is your total return on this investment?
Simplify the Expression. Use only positive exponents. (2x2/5y4)-2
25y8/4x4
From an equation, how can you tell if a function represents exponential growth?
If the b value in f(x)=a(b)x is 1 or greater.
A boat cost $15,465 and the value decreases at a rate of 15% per year. How much will the boat be worth after 5 years?
$6861.90.
Write an equation for the nth term. 5,-10, 20, -40
an=5(-2)n-1 or an=(-5/2)(2)n
Your 6 1/4 year investment of $40,000 at 14% compounded quarterly is worth how much now?
94,529.80